Equation Showdown Notes TEKS A.5(A) Mastery
EQUATION SHOWDOWN
Solving multi-step linear equations with decimals, fractions, and variables on both sides.
NAME:
DATE:
PD:
STAAR Standard
Solve linear equations in one variable, including those with distributive property on both sides.
THE D-C-M-S STEP SYSTEM
D
Distribute
C
Combine
M
Move Var
S
Solve
I DO Problem 1: Solve the Equation Sample 7
Solve the equation below for \(q\):
\(4(q + 56.5) = 30q - 112\)
D
Distribute the 4:
C
Combine Like Terms:
None needed on either side.
M
Move Variables:
S
Isolate and Solve:
SHOW ALL WORK HERE
Student Workspace \(q =\) _______
WE DO Problem 2: Distribute Carefully with Decimals Sample 8
What value of \(n\) makes the equation below true?
\(4(0.5n - 3) = n - 0.25(12 - 8n)\)
D
Distribute BOTH sides:
C
Combine Like Terms (Right):
M
Move Variables:
S
Analyze Solution:
SHOW ALL WORK HERE
Student Workspace Result: _________
Equation Showdown Notes • Standard Mastery Page 1 of 2
TEKS A.5(A) Mastery
EQUATION SHOWDOWN: PRACTICE STEPPING UP
Student Pack
WE DO Problem 3: Double Distribution with Negatives Step Guided
Solve the equation below:
\(-3(2.5x - 4) = 8.5x - 2(3 - x)\)
D
Distribute Both Negatives:
C
Combine Like Terms:
M
Move Variables:
S
Isolate and Solve:
SHOW ALL WORK HERE
Student Workspace \(x =\) _______
YOU DO TOGETHER Minimum Guided Challenges Check off your steps!
PROB 4
What value of \(k\) makes the equation true?
\(0.5(8k - 12) = 1.5(2k + 8)\)
Workspace \(k =\) _______
Step Checklist
Distribute (D) Combine (C) Move Var (M) Solve (S)
PROB 5
Solve the equation:
\(-2(1.5w - 4) = 0.5(4w + 16)\)
Workspace \(w =\) _______
Step Checklist
Distribute (D) Combine (C) Move Var (M) Solve (S)
Equation Showdown Notes • Standard Mastery Page 2 of 2
Equation Showdown Practice TEKS A.5(A) Practice
EQUATION MASTERY SHOWDOWN
Solve each equation. Use the checklist on the right to track each step of your solving process.
NAME:
DATE:
PD:
PROBLEM 1
What value of \(x\) makes the equation true?
\(1.5(4x - 6) = 2x + 9\)
Maximized Work Area
Step Checklist
Distribute Combine Move Var Solve
Final Solution:
\(x =\)
PROBLEM 2
Solve the equation below:
\(-3(2a - 5) = 4a + 25\)
Maximized Work Area
Step Checklist
Distribute Combine Move Var Solve
Final Solution:
\(a =\)
PROBLEM 3
What value of \(y\) makes the equation true?
\(\frac{1}{2}(8y - 12) = 3y + 14\)
Maximized Work Area
Step Checklist
Distribute Combine Move Var Solve
Final Solution:
\(y =\)
Equation Showdown Practice • Standard Mastery Page 1 of 5
TEKS A.5(A) Practice
EQUATION MASTERY SHOWDOWN
Pacing Up Workspace
PROBLEM 4
Solve the equation below:
\(0.8(5h - 10) = 1.2(2h + 5)\)
Maximized Work Area
Step Checklist
Distribute Combine Move Var Solve
Final Solution:
\(h =\)
PROBLEM 5
What value of \(m\) makes the equation true?
\(-0.5(6m + 8) = 2m - 19\)
Maximized Work Area
Step Checklist
Distribute Combine Move Var Solve
Final Solution:
\(m =\)
PROBLEM 6
Solve the equation below:
\(5(2w + 3) = -2(w - 6) + 15\)
Maximized Student Workspace
Final Answer:
\(w =\)
Equation Showdown Practice • Standard Mastery Page 2 of 5
TEKS A.5(A) Practice
EQUATION MASTERY SHOWDOWN
Max Workspaces
PROBLEM 7
What value of \(p\) makes the equation true?
\(\frac{3}{4}(8p - 12) = 2p + 9\)
Maximized Student Workspace
Final Answer:
\(p =\)
PROBLEM 8
Solve the equation below:
\(-4(1.5k + 2.5) = -2(2k - 3) - 10\)
Maximized Student Workspace
Equation Showdown Teacher Key Teacher Resource • Answer Key
EQUATION SHOWDOWN: NOTES KEY
Step-by-step solutions and model responses for teacher guided lessons.
Answer Key Set
Problem 1 (I Do) Equation: \(4(q + 56.5) = 30q - 112\)
Solving Steps:
1. D: Distribute the \(4 \Rightarrow 4q + 226 = 30q - 112\)
2. C: None required.
3. M: Subtract \(4q \Rightarrow 226 = 26q - 112\)
4. S: Add \(112 \Rightarrow 338 = 26q \Rightarrow q = 13\)
Final Solution Block: \(q = 13\)
Problem 2 (We Do) Equation: \(4(0.5n - 3) = n - 0.25(12 - 8n)\)
Solving Steps:
1. D: Distribute both sides \(\Rightarrow 2n - 12 = n - 3 + 2n\)
2. C: Combine terms on right \(\Rightarrow 2n - 12 = 3n - 3\)
3. M: Subtract \(2n \Rightarrow -12 = n - 3\)
4. S: Add \(3 \Rightarrow n = -9\)
Final Solution Block: \(n = -9\)
Problem 3 (We Do) Equation: \(-3(2.5x - 4) = 8.5x - 2(3 - x)\)
Solving Steps:
1. D: Distribute: \(-7.5x + 12 = 8.5x - 6 + 2x\)
2. C: Combine terms on right: \(-7.5x + 12 = 10.5x - 6\)
3. M: Add \(7.5x \Rightarrow 12 = 18x - 6\)
4. S: Add \(6 \Rightarrow 18 = 18x \Rightarrow x = 1\)
Final Solution Block: \(x = 1\)
Problem 4 (You Do)
Equation: \(0.5(8k - 12) = 1.5(2k + 8)\)
D: \(4k - 6 = 3k + 12\)
M: \(k - 6 = 12\)
S: \(k = 18\)
Answer: \(k = 18\)
Problem 5 (You Do)
Equation: \(-2(1.5w - 4) = 0.5(4w + 16)\)
D: \(-3w + 8 = 2w + 8\)
M: \(-5w + 8 = 8\)
S: \(-5w = 0 \Rightarrow w = 0\)
Answer: \(w = 0\)
Equation Showdown Notes Key • Teacher Reference Page 1 of 2
Teacher Resource • Answer Key
EQUATION MASTERY: INDEPENDENT PRACTICE KEY
Practice Problems 1 - 15
PROB 1
\(1.5(4x - 6) = 2x + 9\)
Step: \(6x - 9 = 2x + 9\)
Step: \(4x = 18\)
Answer: \(x = 4.5\)
PROB 2
\(-3(2a - 5) = 4a + 25\)
Step: \(-6a + 15 = 4a + 25\)
Step: \(-10a = 10\)
Answer: \(a = -1\)
PROB 3
\(\frac{1}{2}(8y - 12) = 3y + 14\)
Step: \(4y - 6 = 3y + 14\)
Step: \(y = 20\)
Answer: \(y = 20\)
PROB 4
\(0.8(5h - 10) = 1.2(2h + 5)\)